Optics
When light strikes the interface between two materials, the light generally
divides into two parts: reflected light (angle of incidence=angle of reflection)
and refracted light. In order to find the angle of refraction we use Snell's
Law.
There is another phenomenon called Total Internal Reflection. This is when the light ray enters the medium at its critical angle. This causes the light to bend such that it travels along the surface. Once the critical angle is exceeded, all the light gets reflected, thus no light gets refracted. This is TIR. Fiber-optic cables use this idea of TIR. The inside of the cable consists of glass while the outer layer is cladding. This is very practical in the field of medicine as we use it in such procedures as colonoscopy.
Total Internal Reflection
When light passes from a medium of longer refractive index into one of smaller refractive index (water to air), the refracted ray bends away from the normal.
As the angle of incident (
1)
increases, 2
also increases. When the angle of incident reaches a certain value called the
critical angle (c),
the angle of refraction is 90°. Then the refracted ray points along the
surface.
When the angle of incidence exceeds the critical angle, there is no refracted light. All the incident light is reflected back, a phenomenon called TIR (Total Internal Reflection).
TIR occurs only when light travels from a higher-index medium toward a lower-index medium.
From Snell's law:
Let 1 =
c and 2
=90°
n1sin
Sin
For example, the critical angle for light traveling from water (n1=1.33) to air (n2=1.00) is
For incident angles greater than 48.8°, there is no refracted light and the light is totally reflected back into the water.
Ex. A beam of light is propagating through a diamond (n1=2.42) and strikes a diamond-air interface at an angle of incidence of 28°. (a) Will part of it enter the air ( n2=1.00) or will the beam be totally reflected?
Since 28°>24.4°, there is no refraction. The light is totally reflected
back into the diamond.
(b) If the diamond is in water rather than air?
Since 33.3°>28°, the light beam is refracted into the water.
The Human Eye
The human eye is the most remarkable of all optical devices. Eyeball is approximately
spherical (D=25mm). Light enters the eye through the cornea. The cornea is a
transparent membrane that covers a clear liquid region called the aqueous humor.
Behind this is the iris, the lens, a jelly-like region called the vitreous humor
and finally, theretina. The retina is a light sensitive structure which contains
rods and cones. When they are stimulated, they send electrical impulses to the
brain via the optic nerve. The iris is the colored portion of the eye that controls
the amount of light that gets to the retina.
The Optics of the Eye
The eye and the camera are similar
both have a lens system and a diaphragm.
Retina is same as film.
The image that is formed on the retina is inverted and smaller than the object.
Clear vision-- Eye musts refract the incoming light rays to forma sharp image
on the retina.
Light travels through 5 different media.
| Air --> | Cornea --> | Aqueous Humor --> | The Lens --> | Vitreous Humor |
| n=1.00 | n=1.38 | n=1.33 | n=1.40 | n=1.34 |
Each time light passes from one medium to another, it is refracted.
The greatest amount of refraction (‰70%) occurs at the air/cornea boundary.
The refraction at the other boundaries are small. The lens contributes about
20-25% of the total refraction.
The eye has a fixed image distance. (The distance between the lens and the retina
is constant)
The images are produced on the retina for objects located at different distances since the focal length of the lens is adjustable.
The ciliary muscles adjust the focal length.
Looking at a very distant image
Ciliary muscles relax--> the lens has its longest focal length.
Looking at a very close image.
Ciliary muscles tense. The lens is thicker --> shorter length.
A nearsighted eye (Myopic) -- can focus on nearby objects but not on distant ones. Use diverging lens.
A farsighted eye (Hyperopic)-- can see distant objects clearly. Use converging lens
Accommodation is the process by which the focal length of the eye is automatically adjusted.
The refractive power of a lens is measured in diopters (1/f)
A converging lens has a (+) refractive power
A diverging lens has a (-) refractive power
Ex. A nearsighted person (transparency)
